How to create a circle pie chart with separate (adjustable/variable) triangle "chunks"?
You can also do this with a curve by adding a bevel object and changing the Start/End values of the bevel:




Shift+A> Curve> Circle.
In edit mode of the new curve press Alt+C to 'Toggle Cyclic' so the curve doesn't join its ends together:





Select all the curve points and change their handle type to 'Free' in the side toolbar (T) under 'Handles' and move the curve points back into a circular shape (but the circle will now have a gap).
Extrude the last curve point with E and place it exactly on top of the other end of the curve (a bit more carefully than I have):





Now add a new curve in object mode and flatten it so it is a straight line:





In the curve properties for the curve that is a circle set the 'Bevel Object' to be the curve that is a straight line:





You can now adjust the 'Start' or 'End' values (shown in the first gif) to adjust the 'completeness' of the circle.
As one final step, you can give thickness to the curve by adding a 'Solidify' modifier and then an 'Edge split' modifier to correct the shading:




Duplicate this curve and adjust the 'Start' and 'End' values for each new segment of the pie.